{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#用正态随机过程处理回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这个主题将介绍如何用正态随机过程（Gaussian process，GP）处理回归问题。在线性模型部分，我们曾经见过在变量间可能存在相关性时，如何用贝叶斯岭回归(Bayesian Ridge Regression)表示先验概率分布（prior）信息。\n",
    "\n",
    "正态分布过程关心的是方程而不是均值。但是，如果我们假设一个正态分布的均值为0，那么我们需要确定协方差。\n",
    "\n",
    "这样处理就与线性回归问题中先验概率分布可以用相关系数表示的情况类似。用GP处理的先验就可以用数据、样本数据间协方差构成函数表示，因此必须从数据中拟合得出。具体内容参考[The Gaussian Processes Web Site](http://www.gaussianprocess.org/)。\n",
    "\n",
    "<!-- TEASER_END -->"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##Getting ready"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "首先要我们用一些数据来演示用scikit-learn处理GP："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import load_boston\n",
    "boston = load_boston()\n",
    "boston_X = boston.data\n",
    "boston_y = boston.target\n",
    "train_set = np.random.choice([True, False], len(boston_y), p=[.75, .25])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##How to do it..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "有了数据之后，我们就创建scikit-learn的`GaussianProcess`对象。默认情况下，它使用一个常系数回归方程（constant regression function）和平方指数相关函数（ squared exponential correlation），是最主流的选择之一："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "GaussianProcess(beta0=None,\n",
       "        corr=<function squared_exponential at 0x0000000006F1C950>,\n",
       "        normalize=True, nugget=array(2.220446049250313e-15),\n",
       "        optimizer='fmin_cobyla', random_start=1,\n",
       "        random_state=<mtrand.RandomState object at 0x00000000052A4BA8>,\n",
       "        regr=<function constant at 0x0000000006F15950>,\n",
       "        storage_mode='full', theta0=array([[ 0.1]]), thetaL=None,\n",
       "        thetaU=None, verbose=False)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.gaussian_process import GaussianProcess\n",
    "gp = GaussianProcess()\n",
    "gp.fit(boston_X[train_set], boston_y[train_set])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "其中，\n",
    "\n",
    "- `beta0`：回归权重。默认是用MLE（最大似然估计，Maximum Likelihood Estimation）方法进行估计。\n",
    "- `corr`：相关系数方程。提供了若干种方程，后面会介绍。\n",
    "- `normalize`：默认是`True`，中性化调整样本值，方便应用MLE进行估计。\n",
    "- `nugget`：正则化参数，是可选的，默认是一个很小的值。你可以将这个参数用于每个样本值（参数是一个数值），也可以对样本值使用不同的参数（参数是一个数组，与样本值个数相等）。\n",
    "- `regr`：默认是常系数回归方程。\n",
    "\n",
    "现在让我们拟合对象看看测试效果："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "test_preds = gp.predict(boston_X[~train_set])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "让我们把预测值和实际值画出来比较一下。因为我们做了回归，还可以看看残差散点图和残差直方图。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rkYFzW/LY+2FILR1oHy48z/O8btapEedgJZf9o2wvoe0lGz3Pa6/xi2eSWA8p5YPbPrhf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\nm5mZmZkV4MDZzMzMzKyA/w+wGHPNfLPOHQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x78e0c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "from matplotlib import pyplot as plt\n",
    "f, ax = plt.subplots(figsize=(10, 7), nrows=3)\n",
    "f.tight_layout()\n",
    "ax[0].plot(range(len(test_preds)), test_preds, label='Predicted Values');\n",
    "ax[0].plot(range(len(test_preds)), boston_y[~train_set], label='Actual Values');\n",
    "ax[0].set_title(\"Predicted vs Actuals\")\n",
    "ax[0].legend(loc='best')\n",
    "ax[1].plot(range(len(test_preds)),\n",
    "test_preds - boston_y[~train_set]);\n",
    "ax[1].set_title(\"Plotted Residuals\")\n",
    "ax[2].hist(test_preds - boston_y[~train_set]);\n",
    "ax[2].set_title(\"Histogram of Residuals\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##How it works..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "上面我们快速演示了一下，现在让我们看看这些参数，看看如何优化它们。首先，我们看看`corr`函数的类型。这个函数描述了不同组`X`之间的相关性。scikit-learn提供了5种函数类型：\n",
    "\n",
    "- 绝对值指数函数（absolute_exponential）\n",
    "- 平方指数函数（squared_exponential）\n",
    "- 广义指数函数（generalized_exponential）\n",
    "- 立方项函数（cubic）\n",
    "- 线性函数（linear）\n",
    "\n",
    "例如，平方指数函数公式如下：\n",
    "\n",
    "$$K= \\exp {-\\frac {|d|^2}{2l^2}}$$\n",
    "\n",
    "另外，线性函数就是两个点的点积：\n",
    "\n",
    "$$K=x^T{x'}$$\n",
    "\n",
    "另一个参数是`theta0`，表示参数估计的起始点。\n",
    "\n",
    "一旦我们有了$K$和均值的估计值，过程就完全确定了，因为它是一个GP；之所以用正态分布，是因为在机器学习中它一直很受欢迎。\n",
    "\n",
    "下面我们换个`regr`函数类型和`theta0`参数，看看结果会如何变化："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "gp = GaussianProcess(regr='linear', theta0=5e-1)\n",
    "gp.fit(boston_X[train_set], boston_y[train_set]);\n",
    "linear_preds = gp.predict(boston_X[~train_set])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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+PMkxSXZN8rj+3OalSQ5IcmL/2+2DwI/ppqKnupBuavoVSXYD3sZAINP9zv2CJMuS7E13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\nnGEtSVLjDGtJkhpnWEuS1DjDWpKkxv1/7Mb5uSwRpjkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9563400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(7, 5))\n",
    "f.tight_layout()\n",
    "ax.hist(test_preds - boston_y[~train_set],label='Residuals Original', color='b', alpha=.5);\n",
    "ax.hist(linear_preds - boston_y[~train_set],label='Residuals Linear', color='r', alpha=.5);\n",
    "ax.set_title(\"Residuals\")\n",
    "ax.legend(loc='best');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "很明显，第二个模型的预测效果大部分区间要更好。如果我们把残差汇总起来，我们可以看看MSE预测的结果："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "17.456331927446904"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.power(test_preds - boston_y[~train_set], 2).mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.320038747573518"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.power(linear_preds - boston_y[~train_set], 2).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##There's more..."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "我们可能还想掌握估计的不确定性。在我们预测的时候，如果我们`eval_MSE`设置为`True`，我们就获得MSE的值，这时预测返回的是预测值与MSE估计值的元组。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 5.14026315,  5.30852052,  0.91152632,  2.87148688,  2.55714482])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_preds, MSE = gp.predict(boston_X[~train_set], eval_MSE=True)\n",
    "MSE[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "这样我们就可以计算估计的误差了。让我们画出来看看准确率："
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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V8Qd9ucNwanwS+JJrDe7wlg0wK06/M7X+kZ6RQ/mdKirpyMtrdlxcV7q5al4c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\n9BTsRESk9BTsRESk9P4/XJNEODlddYEAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x9ccb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, ax = plt.subplots(figsize=(7, 5))\n",
    "n = 120\n",
    "rng = range(n)\n",
    "ax.scatter(rng, test_preds[:n])\n",
    "ax.errorbar(rng, test_preds[:n], yerr=1.96*MSE[:n])\n",
    "ax.set_title(\"Predictions with Error Bars\")\n",
    "ax.set_xlim((-20, 140));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "你会看到，许多点的估计都有些变化。但是，前面的数据显示，总体误差不是特别大。"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
